code: def warp_points_tps(
      points_src: torch.Tensor,
      kernel_centers: torch.Tensor,
      kernel_weights: torch.Tensor,
      affine_weights: torch.Tensor,
  ) -> torch.Tensor:
      r"""Warp a tensor of coordinate points using the thin plate spline defined by kernel points, kernel weights, and
      affine weights.
  
      The source points should be a :math:`(B, N, 2)` tensor of :math:`(x, y)` coordinates. The kernel centers are
      a :math:`(B, K, 2)` tensor of :math:`(x, y)` coordinates. The kernel weights are a :math:`(B, K, 2)` tensor,
      and the affine weights are a :math:`(B, 3, 2)` tensor.  For the weight tensors, tensor[..., 0] contains the
      weights for the x-transform and tensor[..., 1] the weights for the y-transform.
  
      Args:
          points_src: tensor of source points :math:`(B, N, 2)`.
          kernel_centers: tensor of kernel center points :math:`(B, K, 2)`.
          kernel_weights: tensor of kernl weights :math:`(B, K, 2)`.
          affine_weights: tensor of affine weights :math:`(B, 3, 2)`.
  
      Returns:
          The :math:`(B, N, 2)` tensor of warped source points, from applying the TPS transform.
  
      Example:
          >>> points_src = torch.rand(1, 5, 2)
          >>> points_dst = torch.rand(1, 5, 2)
          >>> kernel_weights, affine_weights = get_tps_transform(points_src, points_dst)
          >>> warped = warp_points_tps(points_src, points_dst, kernel_weights, affine_weights)
          >>> warped_correct = torch.allclose(warped, points_dst)
  
      .. note::
          This function is often used in conjunction with :func:`get_tps_transform`.
      """
      if not isinstance(points_src, torch.Tensor):
          raise TypeError(
              f"Input points_src is not torch.Tensor. Got {type(points_src)}"
          )
  
      if not isinstance(kernel_centers, torch.Tensor):
          raise TypeError(
              f"Input kernel_centers is not torch.Tensor. Got {type(kernel_centers)}"
          )
  
      if not isinstance(kernel_weights, torch.Tensor):
          raise TypeError(
              f"Input kernel_weights is not torch.Tensor. Got {type(kernel_weights)}"
          )
  
      if not isinstance(affine_weights, torch.Tensor):
          raise TypeError(
              f"Input affine_weights is not torch.Tensor. Got {type(affine_weights)}"
          )
  
      if not len(points_src.shape) == 3:
          raise ValueError(
              f"Invalid shape for points_src, expected BxNx2. Got {points_src.shape}"
          )
  
      if not len(kernel_centers.shape) == 3:
          raise ValueError(
              f"Invalid shape for kernel_centers, expected BxNx2. Got {kernel_centers.shape}"
          )
  
      if not len(kernel_weights.shape) == 3:
          raise ValueError(
              f"Invalid shape for kernel_weights, expected BxNx2. Got {kernel_weights.shape}"
          )
  
      if not len(affine_weights.shape) == 3:
          raise ValueError(
              f"Invalid shape for affine_weights, expected BxNx2. Got {affine_weights.shape}"
          )
  
      # f_{x|y}(v) = a_0 + [a_x a_y].v + \sum_i w_i * U(||v-u_i||)
      pair_distance: torch.Tensor = _pair_square_euclidean(
          points_src, kernel_centers
      )
      k_matrix: torch.Tensor = _kernel_distance(pair_distance)
  
      # broadcast the kernel distance matrix against the x and y weights to compute the x and y
      # transforms simultaneously
      k_mul_kernel = (
          k_matrix[..., None].mul(kernel_weights[:, None]).sum(-2)
      )
      points_mul_affine = (
          points_src[..., None].mul(affine_weights[:, None, 1:]).sum(-2)
      )
      warped: torch.Tensor = (
          k_mul_kernel + points_mul_affine + affine_weights[:, None, 0]
      )
  
      return warped
  
file_path: kornia/kornia/geometry/transform/thin_plate_spline.py
imports: from __future__ import annotations
  import torch
  from torch import nn
  from kornia.core import ones, zeros
  from kornia.utils import create_meshgrid
  from kornia.utils.helpers import _torch_solve_cast
label_desc: Use image node_id 4 for calling a global function with example usage: warp_points_tps(points_src, kernel_centers, kernel_weights, affine_weights) and returns: warped